User blog:Shadow at Morning/Determination of the Size of Vale via Cartographic Analysis
Abstract Via cartographic analysis and comparison to Earth, the sizes of Vale and Remnant were estimated. Using a range of values for the gravity of Remnant, and assuming similar composition to Earth, three different estimates of Remnant's size and that of Vale were produced. Larger than any megalopolis on Earth, and larger than many countries, Vale is truly a gargantuan city. Introduction Remnant is the planet on which RWBY takes place. Because of the nature of the inhabitants of the planet, humanity is principally confined to four cities on the entire planet. These features make Remnant an interesting problem to fictional historians, cartographers, and sociologists. Vale, one of these cities, is the setting of the first several seasons, and is thus the most easily studied city, because of the existence of various maps. As a result, Vale is a topic of interest in the larger discussion of Remnant’s situation, and an attractive area for research. Previous work on the geography of Remnant has been done by The Devil’s Advocate WP and DiegoAnime3000 , who have analysed the geographical features visible on the terrain map, providing insight into human settlement patterns [1 ][2 ], and determined the locations of the kingdoms by means of time zone analysis [3 ]. Additionally, qualitative cartographic analysis was performed by Alex T Snow and FireDart , with the former creating a bounding box around Vale, to the pixel [4 ], and the latter producing variant maps [5 ]. However, there has been little previous work done on determining features of Vale itself, and what previous work has been done [6 ] was revealed to contain significant flaws in the underlying assumptions, leading to a figure for Vale’s size which was off by several orders of magnitude. Therefore, this analysis seeks to determine the approximate size of Vale by analysing the existing maps and comparing them to the size of Earth. Materials and Methods We begin by making a number of simplifying assumptions. The first is that the map projection used for the canonical maps provided is equirectangular. This projection turns meridians into vertical lines of constant spacing and latitudes into horizontal lines of constant spacing. This which causes severe distortion at non-equatorial latitudes. Fortunately, the existing maps all place Vale itself nearly equatorial, so the distortions from the projection will be minimal. The equirectangular projection centered at the equator is the plate carrée, which is a fairly common projection, though more often found in older maps. Nevertheless, it remains a decent assumption, given that fantasy map creators would likely not consider map projection overmuch. However, the maps do not fit the dimensions necessary for an equirectangular projection. This leads to the second assumption, which is that the entirety of the polar angle is represented, but that only a portion of the azimuthal angle is present, and was omitted because it contains only open ocean, with some small islands. This assumption is supported by the globe seen in “Ruby Rose”, which suggests the maps contain the entire polar angle [7 ]. This assumption is further supported by the map in Bartholomew Oobleck's classroom, which, being an in-universe map, would faithfully depict the entire polar regions, which remain absent [8 ]. Given that Remnant possesses routine air travel, mapping the planet from the air in its entirety is assumed to have occurred. The next assumption is that Remnant possesses similar gravity to Earth. We shall here specify that we consider similar gravity to be within .1 g of Earth’s gravity. We shall also assume that the planet Remnant possesses a composition similar to that of Earth, with similar density. The maps used are presented here, and include Equirectangular-projection_SW.jpg [9 ], Rwby_map1.jpg [10 ], Hist2_00002.png [11 ], Remnant_kingdoms_overlay_Vale.png [4 ], and ValeMap.png [12 ]. These are the earliest terrain map of Remnant available, the map from World of Remnant: Kingdoms, and a map blending the two, which was produced by ChishioKunrin and modified by Alex T Snow to bound Vale. These images may be found as figures 1-5. Equirectangular_projection_SW.jpg|Figure 1: An equirectangular projection of Earth. Rwby_map1.jpg|Figure 2: Early terrain map of Remnant. Hist2_00002.png|Figure 3: A map of Remnant from World of Remnant: Kingdoms. Remnant_kingdoms_overlay_Vale.png|Figure 4: A map combining Figures 2 and 3, produced by ChishioKunrin and modified by Alex T Snow. ValeMap.png|Figure 5: Roman Torchwick's map of Vale. ImageJ was used to provide a global scale from the known size of Earth, and apply that scale to an appropriately-resized map of Remnant, to get a map scale. This was then used to determine the size of a bounding box around Vale. This allowed an approximate size of the city to be calculated. Results and Discussion By assuming that Remnant’s gravity is within.1g of Earth’s, and that the planetary composition is the same, we extracted a lower and upper bound for Remnant’s size by rearranging the gravity equation and substituting in density: r=g/(Gρ(4/3)π) The bounds extracted for Remnant's size were 5727 km and 6999 km, which, normalized by Earth's equatorial radius, are .898 and 1.097. We examined both the upper and lower bounds, as well as the case in which Remnant is exactly the size of Earth. Using ImageJ, we set a global scale and applied a scale bar to a plate carrée projection of Earth (Fig. 6), using the equatorial radius of Earth. We then scaled various Remnant maps to the vertical dimension of the plate carrée. This yielded an image significantly smaller in the horizontal dimension than the map of Earth. Using the global scale, a scale bar was then applied to the maps of Remnant, as seen in figures 7-15. A series of test measurements confirmed that all maps were approximately equivalent. The dimensions of these maps can be found in the captions. Rwby_map1 scaled .898.png|Figure 7:Lower bound early terrain map with scale bar. 27217 km by 18117 km. Hist2_00002 scaled .898.png|Figure 8: Lower bound kingdoms map with scale bar. 32206 km by 18117 km. Remnant_kingdoms_overlay_Vale scaled .898.png|Figure 9: Lower bound Kunrin-Snow map with scale bar. 32206 km by 18117 km. Rwby_map1 scaled 1.0.png|Figure 10: Mid-range early terrain map with scale bar. 30306 km by 20183 km. Hist2_00002 scaled 1.0.png|Figure 11:Mid-range kingdoms map with scale bar. 35900 km by 20183 km. Remnant_kingdoms_overlay_Vale scaled 1.0.png|Figure 12: Mid-range Kunrin-Snow map with scale bar. 35800 km by 20183 km. Rwby_map1 scaled 1.097.png|Figure 13: Upper bound early terrain map with scale bar. 33270 km by 22145 km. Hist2_00002 scaled 1.097.png|Figure 14: Upper bound kingdoms map with scale bar. 39365 km by 22145 km. Remnant_kingdoms_overlay_Vale scaled 1.097.png|Figure 15: Upper bound Kunrin-Snow map with scale bar. 39365 km by 22145 km. To determine the size of Vale, we expanded on previous work in the field 4, to obtain an approximate size of Vale. By measuring the edges of the bounding box, we were able to determine the size of the Vale map, which lacks a scale. By using the tape measure functionality of ImageJ, the height of the bounding box was determined for each size of Remnant, the values of which can be found in the captions of figures 16-18, which depict the map of Vale with scale bars. The grid squares found on the Vale map were found to be 130 km, 145 km, and 160 km on an edge. ValeMap scaled .898.png|Figure 16: Lower bound map of Vale with scale bars. 2316 km by 1294 km. ValeMap scaled 1.00.png|Figure 17: Mid-range map of Vale with scale bars. 2588 km by 1440 km. ValeMap scaled 1.097.png|Figure 18: Upper bound map of Vale with scale bars. 2817 km by 1586 km. In figures 16-18, the area of the outlined portion was measured by ImageJ, resulting in a low-end calculation of 990,087 km², a mid-range calculation of 1,244,331 km², and a high-end calculation of 1,457,778 km², which are, respectively, slightly smaller than Egypt, slightly smaller than Angola, and slightly smaller than Mongolia [13 ][14 ][15 ]. These measurements are somewhat inaccurate because they include both water area and land area. The data here collected illustrates the massive scale of the kingdoms on Remnant. Vale is incontestably a megalopolis, larger than any currently existing on Earth. From the tip of the northern peninsula to the headwaters of the long, relatively narrow southern bay is approximately 1800 kilometers using the lower bound. These bodies of water, often assumed to be rivers, must therefore be reclassified as bays. The confluence of the bays represents one of the wider portions of the water system, and the distance from north to south shore there is approximately 25 kilometers. This is approximately the width of the Gulf of Suez. The scale of these bodies of water suggest that port operations can take place virtually anywhere along the shore, and is not limited to the oceanic coastline. Likewise, from Beacon to Signal is approximately the same distance. This casts considerable doubt on the veracity of Ruby Rose's statement in the first episode regarding the visibility of Signal, on Patch, from their current location aboard an aircraft near Beacon [7 ], at approximately building height. The sheer amount of land area available to Vale suggests that its populations is at least in the tens of millions, likely significantly higher. Even accounting for industrial and agricultural operations, there is easily enough room for this many people to live comfortably. In fact, since the entire society lives within the confines of the walls, the city is, like most existing megalopoleis, not entirely urbanized, even in the commercial and residential zones. There would be significant green spaces available as parks, not even necessarily on the order of city parks, but even unto what might be called national parks on Earth. In addition, the elevated highways seen in Volume 2 would be but one of scores of similar highways crisscrossing the nation. Public transit in Vale might consist of a web of nearly-independent subway systems connected by high-speed rail. The scale of Remnant gives clues as to the emergence of Vale as known today. Too large to be planned, and too large to have historically been a single entity, Vale likely emerged from a loose aggregation of hundreds of cities and thousands of villages, which gradually conurbanized into a number of still distant metropoleis, further interlinking to produce megalopoleis, which connected to form Vale. These early settlements were protected by natural barriers, such as cliffs, and likely coastal, and were behind a defensive perimeter which would eventually evolve into the wall dividing Vale from the rest of Vytal, albeit likely far away from its current extent, as humans gradually pushed inland. This analysis also provides insight into the scope of the Mountain Glenn project. As the first recent major expansion, it would have represented a colossal undertaking, necessitating the securing of vast swathes of land around which a perimeter wall could be established. Then, a massive amount of land would have to be cleared of obstruction and a new megalopolis would have to be constructed, with utilities integrated into the rest of Vale. Such an undertaking could last decades before completion. Conclusions Vale as a political entity is an interesting study in fictional cartography as there exist maps of both the world and the city; given that the nation is synonymous with the megalopolis, the question of the precise size naturally arises. Vale, being a city at minimum the size of Egypt, is very nearly larger than comprehension. Certainly, most knowledge of the operation of fictional cities must necessarily be discarded as too limited. By estimating the size of the kingdom, a better appreciation of the what occurs in RWBY may be obtained. This in turn allows the formulation of better theories and a better understanding of the setting. Vale, being one of four kingdoms, provides a baseline for estimating the global population. As Atlas, Mistral, and Vacuo are peers on the world stage, they are likely of similar size and power. As more information comes to light regarding other locations, similar analyses my be done to determine the size of the other kingdoms. Other avenues for future work include formulating theories regarding the logistics of operating a megalopolis, including transportation, sanitation, agriculture, industry, and commercial life within the city. Acknowledgements The author would like to thank The Devil's Advocate WP, for his early efforts to analyse the maps, DiegoAnime3000, for his analysis of time zones, Alex T Snow, for his aid and correction of previous work which served as the basis of this, ChishioKunrin, for her creation of an updated terrain map, Ocomfv, for the suggestion about the globe, the RWBY Wiki community at large, for inspiring such speculation, and the creators of RWBY themselves, for creating an interesting world. Thank you all. References The Devil’s Advocate WP, 9 August 2014: “The Historical Geography of Remnant”. Blog post. The Devil’s Advocate WP, 20 August 2014: “The Historical Geography of Remnant Part 2”. Blog post. DiegoAnime3000, 9 August 2014: “Time Zone of the four kingdoms”. Blog post. Alex T Snow, 26 September 2014: “RWBY: World of Remnant: Kingdoms: Comment 153650”. Comments. FireDart, 3 January 2015: “Maps of Remnant (and more svg stuff)”. Forum post. Shadow at Morning, 13 October 2014: “Volume 2, Chapter 10: The Plot Thickens: Post 140”. Forum post. “Ruby Rose”. RWBY Volume I. 18 July 2013. Rooster Teeth. 9:33,10:30. “Jaundice Part 2” RWBY Volume I. 3 October 2013. Rooster Teeth. 2:12. Strebe, 15 August 2011: “Equirectangular_projection_SW.jpg”. Wikimedia. “RWBY Map1.jpg” RWBY Wiki. 8 November 2012. “Hist2 00002.png” RWBY Wiki. 18 September 2014. “ValeMap.png”. RWBY Wiki. 5 September 2013. Central Intelligence Agency, 2014. “Egypt”. The World Factbook. Central Intelligence Agency, 2014. “Angola”. The World Factbook. Central Intelligence Agency, 2014. “Mongolia”. The World Factbook. Category:Blog posts